Mathematics K–6 · Years 5–6

Length times width: where the area formula comes from

Measurement and space

Practical, model not builtLow risk

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The idea

A rectangle on a centimetre grid holds rows of equal squares, so its area is the number of squares in a row times the number of rows, which is length times width.

What you need

1 cm grid paper and a transparent 1 cm grid overlay
a 30 cm ruler and a 1 m rule
rectangles cut from card: 7 cm by 4 cm, 12 cm by 3 cm, 6 cm by 6 cm, and one with sides 8.5 cm by 4 cm
a tape measure for the classroom floor
a square metre made from newspaper taped together and checked with the metre rule

How to do it

Lay the overlay on the 7 cm by 4 cm card. Count the squares in one row and the number of rows, then count all the squares one by one to confirm.
Measure the sides with the ruler and multiply. Compare with the count. Repeat for the 12 by 3 and 6 by 6 cards.
Lay the overlay on the 8.5 cm by 4 cm card. Count whole squares and half squares, then measure and multiply, and compare.
Measure the length and width of the classroom floor in metres and calculate the area in square metres. Check by pacing one square metre made from newspaper across the room.
Draw a rectangle of area 24 square centimetres in three different ways on the grid and write the multiplication for each.

What you should see

The 7 by 4 card shows 7 squares in a row and 4 rows, 28 squares counted one by one and 28 from 7 times 4. The 12 by 3 card gives 36 and the 6 by 6 card 36 as well, so different rectangles can have equal areas. The 8.5 by 4 card gives 32 whole squares plus 4 half squares, 34 square centimetres, matching 8.5 times 4. A classroom measured as 8 m by 7 m would have 8 times 7, 56 square metres. Rectangles of area 24 include 1 by 24, 2 by 12, 3 by 8 and 4 by 6.

What changes

This activity lists no variables to change, measure and keep the same.

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

Area is found by adding the length and the width.
Two rectangles with the same area must have the same shape.

Safety card

Low riskLearners carry it out

Hazards

tape measure retracting

Controls

retract slowly

Note

No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package is not needed; ordinary classroom supervision under the school's usual risk management.

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

Mathematics K-10 Syllabus (2022), NSW Education Standards AuthorityMA3-2DS-02 MAO-WM-01
Australian Curriculum v9AC9M5M02AC9M6M02

Sources

The pages the author read to write this activity.

All Concept Studio activities